Force-velocity relationship and biochemical-to-mechanical energy conversion by the sarcomere

The intracellular control mechanism leading to the well-known linear relationship between energy consumption by the sarcomere and the generated mechanical energy is analyzed here by coupling calcium kinetics with cross-bridge cycling. A key element in the control of the biochemical-to-mechanical energy conversion is the effect of filament sliding velocity on cross-bridge cycling. Our earlier studies have established the existence of a negative mechanical feedback mechanism whereby the rate of cross-bridge turnover from the strong, force-generating conformation to the weak, non-force-generating conformation is a linear function of the filament sliding velocity. This feedback allows the analytic derivation of the experimentally established Hill's equation for the force-velocity relationship. Moreover, it allows us to derive the transient length response to load clamps and the transient force response to sarcomere shortening at constant velocity. The results are in agreement with experimental studies. The mechanical feedback regulates the generated power, maintains the linear relationship between energy liberated by the actomyosin-ATPase and the generated mechanical energy, and determines the efficiency of biochemical-to-mechanical energy conversion. The mechanical feedback defines three elements of the mechanical energy: 1) external work done; 2) pseudopotential energy, required for cross-bridge recruitment; and 3) energy dissipation caused by the viscoelastic property of the cross bridge. The last two elements dissipate as heat.